Author's Personal Copy Applied and Computational Harmonic Analysis Sparsest Solutions of Underdetermined Linear Systems via Q -minimization for 0 < Q 1
Author's Personal Copy Applied and Computational Harmonic Analysis Sparsest Solutions of Underdetermined Linear Systems via Q -minimization for 0 < Q 1
复制标题
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
S. Foucart;Ming-Jun Lai
中科院分区：
文献类型：
--
作者：
S. Foucart;Ming-Jun Lai
在大多数情况下，作者被允许将他们的文章版本（例如以Word或Tex形式）发布到他们的个人网站或机构存储库。作者需要进一步的信息，有关爱思唯尔的存档和手稿政策，鼓励访问：a r t i c l e i n f o a B s t r a c t我们提出了一个条件的矩阵的一个欠定线性系统，保证该系统的解决方案与最小的q-拟不变也是稀疏的。这推广并稍微改进了1-范数的类似结果。然后，我们引入了一个简单的数值计算方案，以最小的q-拟不变量的解决方案，我们研究其收敛性。最后，我们展示了一些实验的结果表明，q-方法比其他可用的方法性能更好。
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a r t i c l e i n f o a b s t r a c t We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal q-quasinorm is also the sparsest one. This generalizes, and slightly improves, a similar result for the 1-norm. We then introduce a simple numerical scheme to compute solutions with minimal q-quasinorm, and we study its convergence. Finally, we display the results of some experiments which indicate that the q-method performs better than other available methods.